I have managed to successfully incorporate a discrete dividend stream into an FDM Crank-Nicolson-based pricing DLL (thanks in part to help from a few people on this forum.)I get "decent" prices for American options of various maturities. With multiple dividends and longer maturities, though, my answers diverge by a more than comfortable amount. Question #1. Anyone else experience questionable results for longer maturities (1.5 - 3 years)? I am comparing my results to (Techhackers: www.thi.com The binomial tree method.)Question #2. I am reading Topper's book on FEM. I understand the basics but have not yet implemented any pricer. Would this be a recommended approach for such a problem (discrete dividends with free boundary)?Question#3. Speed of computation using the FDM approach is slower than what i intended. I am using C# but even if i migrate to C++ i don't foresee any significant improvements. Would FEM be faster?

QuoteQuestion #2. I am reading Topper's book on FEM. I understand the basics but have not yet implemented any pricer. Would this be a recommended approach for such a problem (discrete dividends with free boundary)?You need Crank's book on Moving boundary problem. I don't know your background but to solve this I reckon you need a MSc/PhD in a specific branch of engineering/numerical analysis (FEM, free bdy). One cannot learn FEM on the fly.QuoteQuestion#3. Speed of computation using the FDM approach is slower than what i intended. I am using C# but even if i migrate to C++ i don't foresee any significant improvements. Would FEM be faster?What is slower? For 1 factor 3 seconds for a FDM is easily achieved.FEM is overkill for this kind of problem, although it works but is a lot of maths (FEM is slower than FDM, also in human costs)I would 1) stick to FDM 2) improve the design and (maybe) 3) do it in C++ (about 20% faster than C#).

So FEM does not add any value in QF?

Thanks Cuch.I have a MSc in Electrical Engineering and Financial Math. I figure that if I spend a few weeks with the relevant books and papers underneath my pillow at night, i should be able to come up with something reasonable. When you say 3 seconds, do you mean 3 seconds for a single option?! (Say a Put maturing in 1.5 years from today with monthly dividends coming in...extreme example). How would someone price an entire book of options on an index then in real time? I assume quite a few funds or prop. shops are doing just such a thing. Edit: I realize that multithreading has to be involved. I was just hoping for faster execution on a single thread.

Hi hgIf you find a relevant article it would be great but from first principles it could be a lot of work. I have 3 chapters in my FDM book on this.hope this helps.

QuoteOriginally posted by: PanniniSo FEM does not add any value in QF?It has much value but it is a quantum jump to learn it compared to FDM. As I said, one cannot learn as bedside lecteur.

To what are you actually comparing your prices with? Note that there are a number of ways in which to model discrete dividends and there is no conclusiveargument which is the 'correct' way. So are you sure about the dividend model that is used to create the prices you compare to?Rgds,Heiko

Very interesting indeed. Thank you all for your comments.I'm sure glad I switched from Engineering into Finance. No standard way of doing anything and no "correct" answers for the most part!Good times...